Putin made the announcement in a message of condolence sent to his Afghan counterpart Ashraf Ghani on Saturday.
"The head of the Russian state strongly condemned this cynical crime committed against peaceful citizens and reiterated readiness to continue the most active cooperation with the authorities and people of Afghanistan in fighting all forms of terrorism," read part of the letter published in a statement released by the Kremlin.
Putin also voiced his sympathies and support to the families of the victims and wished the injured a speedy recovery.
According to Afghanistan’s Interior Ministry 83 people were killed and 260 more injured in the attacks claimed by Daesh.
The United Sates also condemned the attack in “the strongest terms" and offered the Afghan government assistance for investigating the incident.
"The innocent victims today were ... exercising nothing more than their constitutional right of peaceful demonstration," said US State Department spokesman John Kirby."The killers responsible for this bloodshed do not represent the future for Afghanistan and will not prevail."
Ghani has also declared Sunday as a day of national mourning during a live televised speech.
"I promise you I will take revenge against the culprits," he said. "I have ordered the attorney general to set up a commission to investigate this incident."